The space-time behavior of a neutron distribution governed by nonlinear multigroup diffusion approximation is considered in this thesis. Stability criteria for equilibrium states of various reactor feedback models are determined by the methods of Liapunov, semigroup and comparison functions. Comparison of the three approaches are made with respect to applicability to various models as well as computational difficulties associated with the three methods. The models chosen serve as illustrative examples of stability analysis; they also complement the existing examples in literature.

The primary objective of this work is to simplify computational difficulties by the use of generalized mean value theorem for functionals, and functions of several variables. The results are expressed in the form of a theorem for the semigroup method, where a necessary condition for asymptotic stability is proven. It is applied to the problem of xenon oscillations. The use of the generalized mean value theorem in connection with the method by comparison function is also shown to lead to computational simplification. The result is applied to two energy group reactor models with temperature feedback.

A simple numerical example and a comparison of the three methods, together with their variations, is given. The results show that the proposed method of calculating stability conditions leads to more conservative conditions, that is, smaller domains of allowable perturbations. The calculational procedure is, however, simplified in that the equilibrium nonlinear problem does not have to be solved.